A very filling meal.
Butter each gratin dish. Layer the bottoms with diced ham, then chilies, 2-3 dollops of sour cream, and some shredded Jack. Crack 2 eggs for each dish, and pour over sour cream. Continue building layers until everything is used, then spread the remaining shredded Jack cheese on top. Cover each gratin dish with foil, and bake at 350 degrees F. for approximately 15 minutes. Remove foil, and bake for another 10 minutes.
These can be assembled a day ahead of time and refrigerated. If they are assembled a day ahead of time and refrigerated, the eggs will take longer to fully cook.